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Posts by Scott

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math: permutations
couple in 1st row ... 2 ways for 1st row ... 4! ways for 2nd row couple in 2nd row ... 4*5 ways for 1st row ... 4! ways for 2nd row [(4 * 5) + 2] * 4!

math:age
2 s = u 3 (s - 9) = u 3 s - 27 = 2 s

Help me anyone - Pre-Calc
Θ is in radians 20º = (2 π / 18) rad 2340 = ½ (2 π / 18) r² 18 * 2340 / π = r²

math
e = p + 50 time = distance / rate ... 1.6 (1800 / e) = 1800 / p substituting ... 1.6 [1800 / (p + 50)] = 1800 / p solve for p, then substitute back to find e and the times

Calculus - Differentials
the error (in D) is ±.05 A = π D² dA = 2 π D dD = .6 π same difference...

Calculus
h = height up wall d = distance from wall by Pythagoras... h² + d² = 20² differentiating ... 2 h dh/dt + 2 d dd/dt = 0 substituting ... (2 * h * -3) + (2 * d * 4) = 0 ... 8 d = 6 h ... d = ¾ h h² + (¾ h)² = 400 solve for h substitute back...

physics
[16 * cos(20º)] / 4.9 the values in the problem are to 2 significant figures ... not sure about hundredths accuracy

Science
I can be traced back to 3000bc, often go unnoticed, can be overhead, under feet or somewhere in between, evolution has changed me, am lighter than I used to be, and can protect your investment.

Physics
distance = 70 * 5 = 350 km speed = distance / time = 350 / (5 + 2)

Math
3, 5, 9, 15

Physics
N is to the left google "right hand SOLENOID rule"

chemistry
(3 / 2) * 41.0

Math
if r = -2, then the denominator is zero...a big no-no factor the numerator and go with B

Chemistry
1.63 is [SO₂]² ... take the square root

Physics
heat capacity is proportional to mass mass is proportional to volume volume is proportional to the cube of the radius heat cap. ratio is ... 1³:2³

Physics
(a) 2400 + 1800 (b) 1800 / (2400 + 1800)

math
h = 4 mi * tan(5º) = 4 * 5280 ft * tan(5º)

Math
the area of the real world room is (36 / 2.5)² times the area of the plan

Physics
the velocity is half, so the remaining energy (kinetic) is a quarter of the original 3/4 of the energy to penetrate 15 cm it will penetrate another 5 cm

Science
m g h = ½ m v² h = v² / (2 g) h = ½ g t² ... v² / (2 g) = ½ g t² t = v / g .. this is ½ the flight time

Math
6000 = 2500 (1 + r/4)^(10 * 4) 2.4 = (1 + r/4)^40 log(2.4) = 40 log(1 + r/4) .0095053 = log(1 + r/4) 1.002213 = 1 + r/4

physics
the expansion coefficient is ... α = 1.20E-5 m /m·ºK ΔL = 1.20E-5 * 12.5 * (154 - 5) L = 12.500 + ΔL

Physics
energy (work) = 1/2 k x^2 w = 1/2 * 950 N/m * (.06 m)^2

Math
multiplying by 1/3 ... (1/x) / [x^(-2/3)] = 1 / [x^(1/3)] multiplying by x^(-2/3) ... 1/x = [x^(-2/3)] / [x^(1/3)] ... = 1 / [x^(3/3)] = 1/x

physics
units conversion a = v / t d = Vave / t = 30 mph / 3.2 s

Physics
average velocity is ... (.36 + 0) / 2 t = d / v = .8 m / .18 m/s acceleration ... a = .36 m/s / t f = 80 kg * a

Math
f - s = 28 2.5 (f + s) = 2320 f + s = 928 adding equations to eliminate s ... 2 f = 956

chemistry
He⁺ because the greater charge of the nucleus keeps a "tighter" hold on the electron

physic
you need the coefficient of friction to solve this

physic
g = 32.2 ft/s (a) 3.73 * 32.2 = w (lbs) (b) 3.73 * (32.2 + 5.5) = w (c) same as (a) (d) 3.73 * (32.2 - 5.5) = w

General Physics
integration is the correct approach work (energy) = F(x) dx the force goes to zero at √2.6, and then goes negative ... this is also the point of max energy

Algebra 2
they appear to be the same line (colinear)

math 101
145 is one s.d. above the mean 68% of scores are in this range 34% are above the mean 50% of scores are below the mean that leaves 16% of scores above 145

maths
good solution, Steve

maths
actually, slope-intercept is better

maths
find the equations (point-slope) of the diagonals and set them equal

math ratios
1 + 6 = 7 7 k = 21 ... k = 3 3 water and 18 fertiliser

Physics
m g h = .12 J .012 * 9.8 * h = .12

physics
the average speed is 40 m/s so it takes 25 s to cover the km the acceleration is 3.2 m/s² ... 80 m/s / 25 s speed halfway 500 = ½ * 3.2 * t² ... find t and multiply by the acceleration to find the speed half speed 40 m/s / 3.2 m/s² = 12.5 s ...average ...

Math
the Richter scale is logarithmic 10^(8.8 - 5.3)

physics
it takes the 1st stone 2 s to reach its peak and return to the top of the tower, now going downward with the same velocity as the 2nd stone that velocity is 9.8 m/s when it reaches the ground, its velocity is 39.2 m/s...4 s * 9.8 m/s its average velocity is 24.5 m/s ... (9.8...

science
.001 moles / .5 L = .002 M

science
λ =330 m/s / 1E4 cycles/s = 33 mm

physics
the average speed is 10.0 m/s ... 70.0 m / 7.00 s 1st point speed is 5.00 m/s ... 10 = (15 + 5) / 2 acceleration is (10.0 m/s / 7.00 s)

Science
mass * [heat of vaporization + (specific heat * temp change)]

Chemistry
a mole of ANY gas occupies 22.4 L at stp (5.2 / 22.4) * Avogadro's number

Algebra
(3 / 2s) + (1 / s) = 1 / 9 27/2 + 9 = s = 45/2 b = 2/3 s = 15

physics
combined force is 2 kN each pier acts as a fulcrum in a class 2 lever system 6 m * 2 kn = 10 m * f1 4 m * 2 kn = 10 m * f2

math
f + s = 205 5 f + 15 s = 2025 ... f + 3 s = 405 subtracting equations ... 2 s = 200

Physics
1 / R + 1 / 400 = 5 / R 1 / 400 = 4 / R

Chemistry
a liter of solution has a mass of 1.114 kg 20.0% of that is H₃PO₄ ... 222.8 g the molar mass of H₃PO₄ is ... 97.99 g so the moles/L is ... 222.8 / 97.99 the 20.0 means 3 sig fig

Math
g(x) = -2 (2x - 4)³ - 1

Math
f(x) = (x + a) (x + b)² (x + c)³

maths
2 sin(21º) = cos(69º) sin(29º) = cos(61º) so it's twice sin² + cos²

math,maths
x/x + 2/x ≥ .2 1 + 2/x ≥ .2 2/x ≥ -.8 2 ≥ -.8 x -5/2 ≤ x

Math
the distance is the same 10 (s - 21) = 7 s 10 s - 210 = 7s

math
r + b = 365 ... 10 r + 10 b = 3650 9.5 r + 10 b = 3645 subtracting equations ... .5 r = 5

Pre-Calculus 11
squaring ... 9 - 6x + x² = x² - 5 x = 7/3

math
L = w + 5 w * (w + 5) = 500 w² + 5 w - 500 = 0 factoring ... (w + 25) (w - 20) = 0 w = 20 ... L = 25

Physics
heat = mass * temperature change * specific heat for the water heat = 200 g * 7.2 ºC * 1 cal/gºC heat gained by the water is the heat lost by the metal for metal heat = 95 g * 70.8 ºC * s.h. s.h. = (water heat) / (95 * 70.8) be aware of significant figures in ...

Algebra
ln(y) + 5 ln(y+1)

physics
each of the four sides of the square is 5 Ω diagonally, there are two parallel paths of two 5 Ω resistances in series each path is 10 Ω (5 + 5), and the two paths in parallel results in a net resistance of 5 Ω

physics
a hanging spring with a freely hanging mass the force (from gravity) is ... m * g = .98 N k = F / d = .98 N / .01 m = 98 N/m

PHYSICS
multiplying or dividing ...add the percent uncertainties 16 ± 2.25% the cm are cancelled in the division process...it's just a ratio

Algebra
squaring both sides ... 36 = n^(2x) multiplying by n ... 36 n = n^(2x + 1)

Algebra
the drop time is ... t = 132 ft/s / 32 ft/s² it starts from rest, so the average velocity is ... (0 + 132) / 2 ft/s the distance is ... d = drop time * average velocity

Science
going directly from a solid to a gas is called sublimation

Physics
heat = mass * temp change * specific heat make sure the units are consistent

Calculus
the horizontal components of the two ropes' tensions balance each other the combined vertical components equal 400 N sin(60º) = T1v / 400 N T2v = 400 N - T1v cos(60º) = T1h = T2H T2 = √[(T2v)² + (T2h)²]

Chemistry
the iron is oxidized the hydrogen is reduced

Physics
80 C / .001 s = 80000 C/s = 80 kA

Math (Quadratic Equations)
(1 / A) + (1 / B) = 1 / 12 (1 / A) + [1 / (A - 7)] = 1 / 12 12 A - 84 + 12 A = A * (A - 7) 24 A - 84 = A² - 7 A 0 = A² - 31 A + 84 factor the quadratic to find A

Math
-3 is not a root the roots are ... -3±i 4, -3+i, -3-i

Math
the highest exponent is the order...and the number of roots a root is a value that makes the function equal to zero you can test values for roots ... 4 works here divide the function by (x - 4) to factor out the known root ... this leaves a quadratic ... use the quadratic ...

algebra 2-1
30 c + 40 t = 270 ... 3 c + 4 t = 27 12 c + 15 t = 105 solve the system 12 c + 16 t = 108

Analytic geometry
this is a line that is the perpendicular bisector of the line between the given points

Analytic geometry
this is an ellipse the two given points are the foci

CHEMISTRY
the 64 is a good clue the mass ratio of the components is constant amu, or grams, or tonnes ... same ratio

Physics
average velocity is ... (4 + 14) / 2 d = v t

Physics
the horizontal velocity is 6 m/s the total velocity is the vector sum of the horizontal and vertical components using Pythagoras, the vertical velocity must be 8 m/s ... it's a 3-4-5 triangle (6-8-10) B looks good

Science
(a) 7 N - 5 N = (b) the object displaced 2 N of water ... w = m g ... 2 = m * 9.8 ... the volume (in L) is equal to the mass of water (in kg) (c) the 7 N object has the same volume as 2 N of water ... its density is 7/2 water's density

Physics
μ > 85.0 / (30.0 * 9.80)

math
3000 + i = 3000 (1 + .07)⁸

Physics
m g μ = 50 N ... μ = 50 / (10 * 9.8)

Physics
momentum is mass times velocity velocity is ... Vi + (a * t) write their momenta in terms of t set the expressions equal, and solve for t

Chemistry
a mole of ANY gas occupies 22.4 L at STP the formula for ammonia (g) is NH₃ its molar mass is 17.0 g

Pre Calculus
the max is on the axis of symmetry of the parabola t = -b / 2a = -2100 / (2 * -80.6)

Physical Science
heat of fusion for ice ... 79.7 cal/g heat from iron ... 100 g * 72 ºC * 0.11 cal/g⋅ºC divide heat from iron by heat of fusion

Math
the volume of metal is ... v = 4/3 * π * (30³ - 20³) cm³ if the density units are g/cm³ then multiply v by .0078

Math
oops... k = 9 3k = 27

Math
2k + 3k + 5k = 3 * 30 cm 10k = 90 cm ... k = 10 cm a) 3 * k = 30 cm b) 90 cm + D = 4 * 33 cm ... D = 42 cm

Physics
(4 kg / 18 amu) * (1 amu / 1.7E-27 kg) careful of sig figs

Physics
emf - (internal resistance * current) = terminal voltage (Ri * .55) + 5.0 = (Ri * .18) + 5.7 emf - (1.9 * .55) = 5.0

math
x + (12½% x) = Rs. 500 1.125 x = Rs. 500

physics
h = ½ g t² ... t = √(2 * 12.0 / g) v = d / t = 7.35 m / t

physics
h = ½ g t² ... t = √(2 h / g) v = d / t = 13.5 m / t

Chemistry
the concentration is 10 Molar sample size is not a factor

Chemistry
(360 / 180) moles / .200 L = 10 M

Physics
it appears to be a format problem 1/60 = 1.67E-2 rev/s

Physics
it takes 60 s for one revolution so it must be 1/60 r/s

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